It have been observed in [1]} that there is a one-to-one correspondence of local maxima of the potential function defined on the product of simplices (i.e., the mixed action profiles in the game) and mixed Nash equilibria in the congestion games. However, since we have restricted the domain of \(\textsc {GD-FixedPoint}\)  to be the hypercube (rather than product of simplices), this observation is insufficient, and mild additional arguments are required. The proof below provides these additional arguments.
